Question

ch 3.2 - test review
126°
1
2
3
find the measure of ∠1.
find the measure of ∠2.
find the measure of ∠3.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and the given $126^{\circ}$ angle are vertical angles, so $m\angle1 = 126^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle2$ and the given $126^{\circ}$ angle are corresponding angles (assuming the two horizontal lines are parallel). Corresponding angles are equal, so $m\angle2=126^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle3$ and $\angle2$ are supplementary (linear - pair). Since the sum of angles in a linear - pair is $180^{\circ}$, and $m\angle2 = 126^{\circ}$, then $m\angle3=180 - 126=54^{\circ}$.

Answer:

• Measure of $\angle1$: $126^{\circ}$
• Measure of $\angle2$: $126^{\circ}$
• Measure of $\angle3$: $54^{\circ}$